Inverse Curvature Flows of Rotation Hypersurfaces

Autor:	Xianfeng Wang, Yong Wei, Yu Han Jin
Rok vydání:	2021
Předmět:	Pure mathematics Hypersurface Principal curvature Applied Mathematics General Mathematics Initial value problem Inverse Mathematics::Differential Geometry Function (mathematics) Curvature Convex function Second derivative Mathematics
Zdroj:	Acta Mathematica Sinica, English Series. 37:1692-1708
ISSN:	1439-7617 1439-8516
DOI:	10.1007/s10114-021-0015-4
Popis:	We consider the inverse curvature flows of smooth, closed and strictly convex rotation hypersurfaces in space forms $$\mathbb{M}_{k}^{n+1}$$ with speed function given by F−α, where α ∈ (0, 1] for κ = 0, −1, α =1 for κ = 1 and F is a smooth, symmetric, strictly increasing and 1-homogeneous function of the principal curvatures of the evolving hypersurfaces. We show that the curvature pinching ratio of the evolving hypersurface is controlled by its initial value, and prove the long time existence and convergence of the flows. No second derivatives conditions are required on F.
Databáze:	OpenAIRE
Externí odkaz:	https://explore.openaire.eu/search/publication?articleId=doi_________::365a40f902cfaaa4dbde6e4951f50362 https://doi.org/10.1007/s10114-021-0015-4 Zobrazit plný text záznamu Plný text ve formátu PDF